Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{p^2 - 9}{p + 3}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{9} = 3$ So we can rewrite the expression as: $y = \dfrac{({p} + {3})({p} {-3})} {p + 3} $ We can divide the numerator and denominator by $(p + 3)$ on condition that $p \neq -3$ Therefore $y = p - 3; p \neq -3$